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Constructing graphs with no immersion of large complete graphs
Graph immersion minimum degree chromatic number edgeconnectivity Hajos Conjecture Hadwiger Conjecture graph minor
2012/6/29
In 1989, Lescure and Meyniel proved, for $d=5, 6$, that every $d$-chromatic graph contains an immersion of $K_d$, and in 2003 Abu-Khzam and Langston conjectured that this holds for all $d$. In 2010, D...
The p-Domination Number of Complete Multipartite Graphs
p-domination set p-domination number complete multipartite graph
2012/5/9
Let $G=(V,E)$ be a graph and $p$ a positive integer. A subset $S\subseteq V$ is called a $p$-dominating set of $G$ if every vertex not in $S$ has at least $p$ neighbors in $S$. The $p$-domination numb...
Complete enumeration of small realizable oriented matroids
Complete enumeration small realizable oriented matroids Combinatorics
2012/4/18
Enumeration of all combinatorial types of point configurations and polytopes is a fundamental problem in combinatorial geometry. Although many studies have been done, most of them are for 2-dimensiona...